The single coils depend on the dummy pickup for the humcancelling. The two inner control screws that peek through the backplate adjust the humcancelling 'level' per pickup, and you can fiddle around with these until you get the best results.
If you still cannot eliminate the noise, it probably does need The Upgrade - I'm sure if adding (cheap) ferrite beads would already solve the issue, they wouldn't suggest the (expensive) upgrade.